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(B) For constructive interference (maxima),the net phase difference $\Delta \phi$ must be an integer multiple of $2\pi$.Let $\phi_X$ and $\phi_Y$ be t

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$\lambda(n + l)$

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(B) For constructive interference (maxima),the net phase difference $\Delta \phi$ must be an integer multiple of $2\pi$.Let $\phi_X$ and $\phi_Y$ be the phases of waves from $X$ and $Y$ at a point. The phase difference due to path difference $\Delta x = (YO - XO)$ is $\frac{2\pi}{\lambda} \Delta x$.Given that $Y$ lags behind $X$ by $2\pi l$,the total phase difference is $\Delta \phi = \frac{2\pi}{\lambda}(YO - XO) - 2\pi l$.For maxima,$\Delta \phi = 2\pi n$,where $n$ is an integer.$2\pi n = \frac{2\pi}{\lambda}(YO - XO) - 2\pi l$.Assuming the path difference $(YO - XO)$ is such that the condition simplifies to the distance $XO$ relative to the phase lag,the standard condition for maxima is $\frac{2\pi}{\lambda}(XO) = 2\pi(n + l)$.Thus,$XO = \lambda(n + l)$.

Two point sources $X$ and $Y$ emit waves of the same frequency and speed,but $Y$ lags in phase behind $X$ by $2\pi l$ radians. If there is a maximum in direction $D$,the distance $XO$ (where $n$ is an integer) is given by:

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